Star Formation with Radiative Transfer

Matthew R. Bate

These calculations take my star cluster calculations to a new level of
complexity, modelling the collapse and fragmentation of 50 solar mass
clouds but including radiative feedback from the young protostars.
The initial conditions were identical to those in the original calculation
and the second hydrodynamical calculation that I performed. Radiative feedback
dramatically reduces the number of objects formed and results in a higher
ratio of stars to brown dwarfs.

Animations

There are four movies, two for each of the two calculations. In each case,
the first movie shows the gas density and temperature evolution for the radiation
hydrodynamical calculation. The second movie in each case compares the
evolution of the density without and with radiative feedback (i.e. compares
the earlier hydrodynamical simulation with the radiation hydrodynamical
simulation). A movie
from 2005 also compares the density evolution of the
original two hydrodynamical calculations.

The animations below both use my typical red-yellow-white
colour scheme to visualise the column density through the star-forming
cloud (left) and my blue-red-yellow-white colour scheme (right) to visualise
temperature (actually mass-weighted temperature integrated through the cloud).

Calculation 1: re-run of the original star cluster formation simulation

Movie of the first radiation hydrodynamical star cluster formation calculation.

Copyright: The material on this page is the property of Matthew Bate.
Any of my pictures and animations may be used freely for non-profit
purposes (such as during scientific talks) as long as appropriate
credit is given wherever they appear. Permission must be obtained
from me before using them for any other purpose (e.g. pictures for publication
in books).

Notes on formats:Quicktime: Plays directly in Powerpoint on an Apple computer. Can be played under Windows by downloading the FREE Quicktime player from Apple. Some version can be played under Unix/Linux using xanim.

Technical Details

The calculations model the collapse and fragmentation of 50 solar mass
molecular clouds that are 0.375 pc or 0.180 pc in diameter (approximately 1.2 and 0.6 light-years, respectively).
At the initial temperature of 10 K with a mean molecular weight of 2.38, this
results in an thermal Jeans mass of 1 solar mass. The free-fall time of the
first type of cloud is 190,000 years and the simulations cover 266,000 years.
The free-fall time of the
denser cloud is 63,400 years and the simulations cover 89,000 years.

The clouds are given an initial supersonic `turbulent' velocity
fields in the same manner as Ostriker, Stone & Gammie (2001).
We generate a
divergence-free random Gaussian velocity field with a power spectrum
P(k) \propto k-4, where k is the wave-number.
In three-dimensions, this results in a
velocity dispersion that varies with distance, lambda,
as sigma(lambda) \propto lambda1/2 in agreement with the
observed Larson scaling relations for molecular clouds (Larson 1981).
This power spectrum is slighly steeper than the Kolmogorov
spectrum, P(k)\propto k11/3. Rather, it matches the
amplitude scaling of Burgers supersonic turbulence associated
with an ensemble of shocks (but differs from Burgers turbulence
in that the initial phases are uncorrelated). The two calculations use the
same initial velocity field.

The calculations were performed using a parallel three-dimensional
smoothed particle hydrodynamics (SPH)
code with 3.5 million particles on the
United Kingdom Astrophysical Fluids Facility (UKAFF) and the University of Exeter Supercomputer. They each took approximately 40000 CPU hours running on 8 to 16
processors.
The SPH code was parallelised using OpenMP by M. Bate. The code uses
sink particles (Bate, Bonnell & Price 1995) to model condensed objects
(i.e. the stars and brown dwarfs). Sink particles are point masses that
accrete bound gas that comes within a specified radius of them. This
accretion radius is to set 0.5 AU. Thus, the calculation resolves circumstellar
discs with radii down to approximately 1 AU.